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Dynamic Control and Optimization of Distributed Energy Resources in a Microgrid

Trudie Wang, Dan O'Neill, Haresh Kamath

arXiv:1410.0054v1math.OC

TL;DR

The paper tackles real-time coordination of many renewable-rich DERs without relying on centralized control. It combines ADMM with MPC to manage a commercial microgrid, and simulations using real data show comparable distributed and centralized performance while preserving device functionality and responding to external conditions.

  • Problem

    Renewable variability and increasing DER scale create a need for decentralized real-time coordination that handles system complexity while maintaining DER functionality and constraints.

  • Method

    The method combines ADMM and MPC to distribute microgrid optimization among independent DERs using local information and simple message exchanges.

  • Results

    Less than 1.5% separates ADMM from centralized total system costs, while both differ from centralized prescient performance by less than 3.3%.

  • Takeaways & Limitations

    Distributed control allows the simulated microgrid to retain device functionality while responding to prices, line limits, and contingency events with minimal information sharing.

Abstract

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As we transition towards a power grid that is increasingly based on renewable resources like solar and wind, the intelligent control of distributed energy resources (DER) including photovoltaic (PV) arrays, controllable loads, energy storage and plug-in electric vehicles (EVs) will be critical to realizing a power grid that can handle both the variability and unpredictability of renewable energy sources as well as increasing system complexity. Realizing such a decentralized and dynamic infrastructure will require the ability to solve large scale problems in real-time with hundreds of thousands of DERs simultaneously online. Because of the scale of the optimization problem, we use an iterative distributed algorithm previously developed in our group to operate each DER independently and autonomously within this environment. The algorithm is deployed within a framework that allows the microgrid to dynamically adapt to changes in the operating environment. Specifically, we consider a commercial site equipped with on-site PV generation, partially curtailable load, EV charge stations and a battery electric storage (BES) unit. The site operates as a small microgrid that can participate in the wholesale market on the power grid. We report results for simulations using real data that demonstrate the ability of the optimization framework to respond dynamically in real-time to external conditions while maintaining the functional requirements of all DERs.

I. INTRODUCTION

The paper addresses decentralized, real-time coordination of renewable-rich microgrids with diverse DERs while preserving device functionality and system constraints. It combines ADMM and MPC to autonomously schedule DERs and adapt to prices, physical limits, and contingencies.

  • Renewable penetration of roughly 10−30% and above challenges existing centralized dispatch because supply is variable and unpredictable.
  • Intelligently coordinated DERs can provide flexibility, reliability, stability, and resiliency, but grid-service use may strain devices or accelerate degradation.
  • The proposed method manages workplace EV charging at a commercial site with PV, partially curtailable load, and battery storage.
  • ADMM within MPC distributes optimization across independent DERs, requiring local state information and simple neighbor messages while accommodating objectives, constraints, and uncertainty.
  • EV owners can define utility functions that balance charging benefits, vehicle utility, lifetime degradation, and privacy without requiring external scheduling control.
  • The study uses real wholesale-price, PV, load, and EV data to evaluate distributed dynamic microgrid operation.

II. MODEL

The model represents a commercial microgrid containing load, PV, EVs, BES, and the grid connection, with schedules and constraints governing power flows. It uses DC power-flow assumptions and device-specific operating objectives.

  • A. System dynamics and constraints: The microgrid includes onsite load, PV generation, NEV EVs, a BES unit, and a PCC modeled as a DER with objectives and constraints.
  • A. System dynamics and constraints: The model uses DC power without phase-schedule constraints, while AC extension requires an additional phase constraint for each DER.
  • 1) Electric load:: Load follows a predicted diurnal profile and may be curtailed between βˆpload and ˆpload, with β specifying the minimum time-dependent fraction served.
  • 1) Electric load:: Load curtailment incurs a penalty weighted by αload.
  • 2) Photovoltaic (PV) array:: PV generation follows a predicted diurnal profile, is represented by nonpositive power, and may be curtailed when it cannot be exported or stored.
  • 2) Photovoltaic (PV) array:: PV curtailment incurs a penalty weighted by αPV.
  • 3) Battery Electric Storage (BES):: BES power can be positive or negative because the unit can charge and discharge, subject to charging and discharging rate limits.

3) Battery Electric Storage (BES).:

The BES model captures bidirectional power exchange, state-of-charge dynamics, capacity limits, cycling costs, and optional terminal conditions. These constraints support storage for PV energy, price hedging, buffering, and grid events.

  • 3) Battery Electric Storage (BES):: BES charging and discharging are limited by rate constraints, with pBES representing its power schedule.
  • 3) Battery Electric Storage (BES):: The BES state of charge evolves through a time-indexed dynamics equation over t = 1, . . . , T.
  • 3) Battery Electric Storage (BES):: Storage and charging efficiencies are bounded in [0, 1], while qBES tracks normalized charge and remains within battery capacity limits.
  • 3) Battery Electric Storage (BES):: A cycling penalty can discourage excessive BES charge-discharge cycles.
  • 3) Battery Electric Storage (BES):: An optional terminal constraint can require final storage to equal 0.5Qcap or the battery’s initial charge state.
  • 4) Electric vehicle (EV):: EVs combine flexible charging and storage but add availability and required-charge constraints tied to arrival, departure, and initial charge state.

4) Electric vehicle (EV):

The EV model treats vehicles as flexible storage-capable loads whose schedules must respect charging limits, battery capacity, availability, and desired departure charge. Owner utility and cycling penalties shape individual scheduling decisions.

  • 4) Electric vehicle (EV):: Each EV has a maximum charge/discharge rate, represented by the vehicle-specific rate parameter.
  • 4) Electric vehicle (EV):: EV storage and charging efficiencies lie in [0, 1], while charge states remain between minimum and maximum battery levels.
  • 4) Electric vehicle (EV):: The desired state of charge qdes,i represents vehicle utility, and αdes,i weights flexibility in failing to meet the desired departure charge.
  • 4) Electric vehicle (EV):: Vehicle utility functions can be learned or specified so owners assign values to charging services and maximize net benefits.
  • 4) Electric vehicle (EV):: A vehicle-specific cycling penalty can weight excessive battery cycling against the owner’s utility function.
  • 4) Electric vehicle (EV):: The PCC applies wholesale rates and caps power transmitted over the line through a power-limiting constraint.

5) Grid connection:

The grid-connection objective coordinates energy-cost minimization with smoother power exchange at the PCC, subject to feasible schedules and power-flow balance.

  • 5) Grid connection:: Negative grid power represents electricity sales to the grid, whereas positive power represents electricity drawn from it.
  • 5) Grid connection:: The PCC objective minimizes wholesale energy cost together with output-regulation cost.The energy term uses the real-time wholesale price schedule, while the regulation term penalizes nonsmooth PCC output.
  • 5) Grid connection:: The smoothness term penalizes the range, slope, and curvature of PCC power output.The corresponding parameters are αrange, αdiff, and αcurv.
  • 5) Grid connection:: The separable system objective sums controller-specific objectives and is minimized subject to power-flow balance.
  • 5) Grid connection:: A schedule is feasible when every controller has finite cost and the power-balance constraint is satisfied.The onsite controllers include load, PV, BES, PCC, and EVs.

C. Control policy

The control policy uses ADMM to distribute each time-step optimization across DER controllers, while exchanged quantities coordinate local schedules toward system-wide power balance and equilibrium.

  • C. Control policy: Each controller uses local states, parameters, constraints, and available external information to determine its control actions.The PCC can access real-time wholesale prices or contingency status, while DERs use their own states and historical profiles.
  • C. Control policy: ADMM distributes the optimization among independent DER controllers within an MPC framework.
  • C. Control policy: ADMM updates local variables and shared copies iteratively to enforce consensus and power-flow feasibility.The formulation introduces copied variables and separates local objectives while retaining the shared balance constraint.
  • C. Control policy: The proximal regularization penalizes deviations from an iterative target and gradually vanishes as schedules converge.
  • C. Control policy: Controllers send updated schedules to a collector, which computes imbalance and broadcasts adjustments to the scaled price.The price rises with net demand and falls with net generation, pushing schedules toward equilibrium.
  • C. Control policy: The paper does not evaluate ADMM convergence rates or scalability in this study.
  • C. Control policy: Internal price signals align locally optimized policies with system objectives while reducing communication and supporting autonomous operation.

B. Model Predictive Control (MPC)

MPC repeatedly solves the decentralized ADMM problem over a future horizon, executes only the first scheduled action, and replans as measurements and operating conditions change.

  • B. Model Predictive Control (MPC): MPC dynamically controls each DER by solving the optimization at every time step.ADMM supplies the decentralized solution used to determine each controller’s action policy.
  • B. Model Predictive Control (MPC): At each step, controllers compute conditional power schedules over a finite horizon and execute only the first action.
  • B. Model Predictive Control (MPC): The process repeats with new state measurements, predictions, and external information to adjust subsequent schedules.This repeated replanning helps accommodate measurement errors, missing information, and inaccurate forecasts.
  • B. Model Predictive Control (MPC): Algorithm 1 initializes storage states, updates forecasts and EV parameters, solves ADMM, and advances the BES and EV states.
  • B. Model Predictive Control (MPC): MPC refits forecasts using updated information and directly incorporates objectives and constraints without trial-and-error controller tuning.
  • B. Model Predictive Control (MPC): A regularization term discourages large changes from the previous solution and promotes smoothness across successive MPC iterations.

IV. PREDICTIONS

The prediction process supplies estimates of unknown inputs for decentralized optimization, while repeated MPC updates allow the controller to correct earlier forecast errors.

  • IV. PREDICTIONS: ADMM-MPC requires estimates of input variables at each time step to determine finite-horizon control policies.Estimates may use historical data or stochastic models, while only general trends are needed for robust operation.
  • IV. PREDICTIONS: MPC dynamically adjusts and self-corrects schedules after executing the first planned action, accommodating past errors or missing information.
  • IV. PREDICTIONS: Prediction accuracy need not be exact because schedules are recalculated at every time step.

A. Power profiles

The paper predicts PV and load profiles over the MPC horizon using historical patterns, smoothing, periodicity, and residual-based error correction. These forecasts capture daily trends and adapt to sudden deviations for dynamic scheduling.

  • PV prediction: PV prediction combines a 24-hour periodic baseline with asymmetric fitting, curvature smoothing, and residual correction.The baseline is reconstructed from historical data, then adjusted for transient weather effects using recent residuals.
  • PV prediction: The PV baseline solves a regularized convex problem that weights positive deviations more heavily toward the outer envelope of fluctuating data.A periodicity constraint enforces Tperiod = 24hrs while curvature regularization smooths the reconstructed profile.
  • Error correction: Residual corrections use a linear model of previous residuals, with future corrections reduced by λ at each time step where 0 < λ < 1.The weights are obtained from a least-squares problem with analytical solution a = M †b.
  • Load prediction: Load prediction uses a similar historical-profile approach, weighting positive and negative deviations equally because both are expected to occur.MPC adaptability allows the forecasts to support dynamic power scheduling despite prediction error.
  • Forecast behavior: Predictions capture diurnal trends, general profile shape, and sudden changes near the measurement time through error correction.The correction pulls the baseline toward the actual output when rapid deviations can be anticipated.

B. EV parameters

EV parameters are predicted from arrival status and historical vehicle data when vehicles have not yet arrived. Stationary distributions provide practical estimates, while desired departure charge is selected conservatively.

  • Prediction basis: For an arrived EV, θEV,i is known; otherwise, its stochastic variables are predicted from available data.The authors expect predictions to improve as accumulated data produce more stationary distributions.
  • Forecast context: The simulations include a figure showing PV and electric-load predictions over the MPC horizon, rather than EV-specific parameter curves.The caption identifies PV output as the top plot and electric load as the bottom plot.
  • Time parameters: Arrival and departure times use maximum-likelihood estimates from stationary probability distributions.Time-dependent Markov models added insignificant or no benefit because MPC already corrects prediction error.
  • Charge-state parameters: Initial and desired departure charge states are estimated with stationary distributions because charge state is not assumed strongly and independently correlated with time variables.qinit is updated daily for vehicles that have not arrived.
  • Charge-state parameters: Desired departure charge uses the highest charge state in its distribution to cover the majority of contingency situations.The authors describe this choice as overly conservative for plug-in hybrids that can use gasoline.

V. NUMERICAL EXAMPLE

The numerical example simulates a Northern California commercial microgrid using real load, PV, and wholesale-price data. It includes a 24-hour MPC horizon, a constrained grid connection, rooftop PV, and a fleet of EVs with specified charging and battery assumptions.

  • Data and horizon: The simulations use real load and generation data from May 18–25, 2013, together with CAISO day-ahead hourly wholesale prices.Each scenario uses T = 96, representing 15-minute intervals over a 24-hour MPC horizon.
  • Site configuration: The microgrid connects through a bidirectional meter with real-time wholesale-price access and a 200kW PCC transfer constraint.Commercial-site load measurements and co-located rooftop PV data come from Northern California.
  • EV fleet: The modeled fleet contains 20 EVs capable of level 2 charging at 7.2kW without a dedicated circuit.EV battery efficiency values ηEV,i are set to 90%.
  • Battery assumptions: Vehicle battery capacities are based on individual travel data, using the longest trip distance, a 2× buffer, and 0.311kWh/mile.Minimum and maximum charge states are set to 30% and 90% to avoid deep cycling.

VI. RESULTS

Over three simulated days, ADMM produced microgrid behavior close to centralized optimization while coordinating DERs around line capacity, prices, renewable variability, and load demands. Storage and EV flexibility reduced curtailment and shaped power flows, while the resulting profiles remained reliable and consistent.

  • Cost comparison: Less than 1.5% separated ADMM from centralized optimization in total system costs, while both were within 3.3% of the centralized prescient case.The simulations covered a three-day period and included ADMM, centralized, and centralized-prescient scenarios.
  • Microgrid power profile: The PCC profile was shaped primarily by the binding line-capacity limit, with DERs absorbing excess PV generation and sustaining load when PV output declined.The optimized profile showed fewer intermittent spikes than the unoptimized PV-and-load base profile.
  • Energy shifting: Storage and EVs discharged slightly as PV initially failed to meet rising load, then shifted PV energy from its noon peak toward the 5PM peak-price period.This scheduling offset the load during the peak-price period and increased net profit.
  • Curtailment: PV curtailment occurred around peak generation hours, while evening load curtailment occurred after solar production ended and import capacity was reached.Curtailment remained small because BES and EV storage minimized these effects.
  • Storage operation: The BES deeply discharged during daily peak prices and recharged as prices fell and PV output increased, while aggregate EVs charged during decreasing prices and discharged during increasing prices.The EV aggregate formed a smoother profile despite individual arrival, departure, and charging constraints.
  • Operating outcomes: Distributed DER scheduling produced reliable, consistent power profiles with intermittent solar when appropriate incentives were provided.The paper identifies improved power quality, higher load factor, and real-time price responsiveness as associated operating outcomes.

VII. CONCLUSION

The paper develops an MPC–ADMM framework that decentralizes microgrid optimization among PV, curtailable load, EV charging, and stationary battery resources. Simulations with real-world data show that the framework preserves device functionality while adapting to prices, line limits, and contingency events with minimal information sharing.

  • Framework: The MPC–ADMM framework distributes and decentralizes microgrid optimization across PV, curtailable load, EV charge stations, and stationary BES resources.It uses local information and simple prediction methods while incorporating additional system and DER information as conditions evolve.
  • Framework: The distributed approach makes microgrid management more tractable through cooperation among resources while respecting coupling constraints from capacity-limited lines.
  • Simulation results: Simulations using campus and transportation data demonstrate that devices retain functionality while the microgrid responds to external prices, physical line limits, and contingency events.
  • Simulation results: With minimal information sharing, the distributed framework achieves performance comparable to centralized optimization using prescient knowledge.
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